Solving Inequalities in One Variable
📘 Key Definitions
Solution of an Inequality: A value of the variable that makes the inequality a true numerical statement. For example, $x = 5$ is a solution of $x > 3$ because $5 > 3$ is true.
Solving an Inequality: Finding all values that satisfy the inequality, or proving that no such values exist.
Equivalent Inequalities: Two inequalities that have exactly the same solution set. For example, $2x > 6$ and $x > 3$ are equivalent.
Domain of an Inequality: The set of all values for which both sides of the inequality are defined.
🔣 Inequality Symbols Review
| Symbol | Meaning | Example | Number Line |
|---|---|---|---|
| $<$ | Less than | $x < 5$ | Open circle, arrow left |
| $>$ | Greater than | $x > 3$ | Open circle, arrow right |
| $\leq$ | Less than or equal to | $x \leq 5$ | Closed circle, arrow left |
| $\geq$ | Greater than or equal to | $x \geq 3$ | Closed circle, arrow right |